Reckoner for demonstrating arithmetical calculations



Aug. 23, 1960 v. KNEFELI 2,949,681

RECKONEIR FOR DEMONSTRATING ARITHMETICAL CALCULATIONS Filed Jan. 5, 1959 3 Sheets-Sheet 1 VITUS KNEFELI ATTORNEY V. KNEFELI Aug. 23, 1960 RECKONER FOR DEMONSTRATING ARITHMETICAL CALCULATIONS 3 Sheets-Sheet 2 Filed Jan. 5, 1959 jm eflarz" VlTUS KNEFELI Arf/wr 0 K/e/n ATTORNEY Aug. 23, 19% v. KNEFELI 49,681

RECKONER FOR DEMONSTRATING ARITHMETICAL CALCULATIONS Filed Jan. 5, 1959 I s Sheets-Sheet s jfiyemorr' VITUS KNEFELI Ar'T/Iur' O K/e/n ATTORNEY RECKONER FOR DEMONSTRATING ARITHlVlETICAL CALCULATIONS Vitus Knefeli, 42 Fullener Strasse, Meppen (Ems), Germany Filed Jan. 5, 1959, Ser. No. 785,007

Claims priority, application Germany Jan. 4, 1958 4 Claims. (Cl. 35-30) This invention relates to a manipulative reckoner intended as a visual aid in primary and secondary school education.

A known reckoner consists of a circular board, disc, or dial, of plywood or the like, having a pin projecting from its center, and slots, notches, or the like, cut at certain angular intervals into its rim, and attached to the back of the board, cords, preferably of rubber, which can be pulled through said notches over the rim and fastened with their free ends to the pin or taken around the pin and fastened to some other notch.

The back of this reckoning board is fitted with means for detachably affixing it to a blackboard or a Wall.

It is a general object of the present invention to improve this useful type of reckoner so that it can be applied to a wider range of arithmetical calculations.

It is a further, more specific, object of the present invention to provide a manipulative reckoner that can visually indicate fractions in units of hundreds or thousands.

It is yet another specific object of the present invention to provide a manipulative reckoner that can visually indicate fractions in units of angular degrees.

To this end the invention consists in the provision of supplementary smaller dials or discs with angular divisions that differ from those marked oil? on the principal board, said supplementary discs being adapted to be hung on the center pin over the face of the principal board and to be secured thereto by rubber cords clipped into the notches in such manner as not to obscure the peripheral markings on the principal board.

In an alternative form of construction the reckoner is embodied in a small hand device with a substantially smaller principal board, simpler in design and therefore cheaper to make than the above described reckoner which is intended for purposes of classroom demonstration.

Preferably this smaller type of reckoner has a principal board with a pin which projects from both sides, readings being taken with the aid of one or several rubber bands which are placed round the projecting pin and through any notches that may be selected.

The novel features which are considered as characteristic for this invention are set forth in particular in the appended claims. The invention itself, however, both as to its construction and its method of operation, together with additional objects and advantages thereof, will be best understood from the following description of two specific embodiments when read in connection with the accompanying drawings in which Fig. 1 is a view of the face of a type of reckoner already known to the art.

Fig. 2 is a back view of this reckoner.

Fig. 3 is a reckoner of the kind shown in Fig. 1, but fitted with a supplementary disc according to one embodiment of the invention,

Fig. 4 is a view of the same reckoner as that illustrated in Fig. 3, fitted with a diiferent supplementary disc,

Fig. 5 is a reckoner, according to another embodiment of this invention, constructed in the manner shown in Fig.

1, but simplified and reduced in size to serve as a small hand reckoner, and

Fig. 6 is a section taken on the line VI--VI in Fig. 5.

Referring now specifically to the drawings, the reckoner illustrated in Fig. 1 consists of a circular board 1, about 22 inches in diameter, consisting of plywod or other suitable material. The center of the circular board has a pin 2, whereas its rim 1 is provided with notches 3 which are angularly placed in such a way that rubber cords stretched from these notches 3 to the central pin 2 will divide up the area of the circular board into segments 5.

The location of the notches 3 around the rim 1 of the board is such as to permit the face of the board to be divided into halves, quarters, eighths, thirds, sixths, ninths, twelfths, fifths, tenths and fifteenths. longing to each of several groups representing fractions- /2, A, i.e. twos-(Va, /6, A,, A i.e. threes-(Vs, A0, A i.e. fives-are identified by like-coloured circles. In Fig. 1 the twos group is indicated by a solid circle, the threes group by a ring, and the fives group by a hatched circle placed below each of the relative notches. The greater the circular mark, the greater the relative fraction. The large circles 6 and '7 at the top and the bottom indicate halves, the medium sized circles 8 and 9 at the right and the left indicate quarters, and the small circles 10 indicate eighths. The appropriate denominator is stamped into the center of each one of the circles.

As shown in Fig. 2 a number of loose rubber cords 4 is attached to a frame 11 at the back of the board. The free end of each rubber cord 4 carries an eyelet ring 12. To permit this fractional reckoner to be readily hung up or secured to a blackboard, the back of the board 1 of the reckoner is equipped with holding devices in the form of suction discs 13 and a wire hook. The reckoner so far described is already known and the invention now relates to the further improvement of this device.

As illustrated in Figs. 3 and 4 supplementary discs 14 and 15 can be mounted on the center pin 2 over the face of the circular board 1 and secured thereto by rubber cords 16 which are clipped into the notches 3.

The supplementary disc shown in Fig. 3 is divided into hundredths at 17 and into thousandths at 18. This arrangement permits the relationship between a proper fraction and parts per hundred or parts per thousand and decimal fractions to be clearly demonstrated in a manner that can be easily grasped by young pupils. For instance if cord 4, as shown in Fig. 3, is stretched through the notch representing 4, the corresponding reading on scale 17 will be twenty-five, thus demonstrating the equivalence of twenty-five and A and the identity of A with 0.25. Scale 18 which is divided into thousandths can be used in an analogous way.

The supplementary disc shown in Fig. 4 carries a scale 19 of 360 divisions which permits the relationship between angular degrees and fractions on a dial to be readily illustrated.

The reckoner according to Figs. 5 and 6 is a simplified version of that shown in Figs. 1 and 2 and is intended to be held in the hand. Consequently its diameter is very much smaller, the face of this reckoner measuring only about 8 inches across. It likewise consists of a circular dial or disc 20 with notches 3 cut into its rim in angular positions representing various fractions, as is the case in the reckoner shown in Fig. 1. However the center pin 21 projects from both sides of the disc 20 and in the illustrated embodiment the pin actually consists of a screw secured to the disc by a nut. Readings are taken with the aid of an endless rubber band of the kind normally used for securing a package, the rubber band being stretched over the pin 21 and through any two notches 3. The supplementary discs 14 and 15 which are used in con- Patented Aug. 23, I960 The notches 3 be-' junction with this embodiment have similar subdivisions as those already described.

The present invention permits the known reckoner for demonstrating calculations with fractions to be applied to a much wider range of arithmetical calculations, and this result is achieved with the simplest of means.

Although the present invention has been described in conjunction with pre ferred embodiments, his to be understood that modifications and variations may be resorted to without departing from the spirit and scope of the invention, as those skilled in the art will readily understand. Such modifications and variations are considered to be within the purview and scope of the invention and appended claims.

What I claim is:

1. A manipulative reckoner for visually aiding in edu-.

face" of said first circular board, the shortest distance from the center of said first circular board to the circumferential periphery thereof being substantially larger than tended across the front face of said first circular board and removably secured to said centrally projecting pin, said band also being adapted to be pulled through any one notch of said plurality of notches and radially extended across the front face of said first and second circular board, pulled around said centrally projecting pin and then removably secured to said first circular board at the location of another one notch of said plurality of notches.

2. The manipulative reckoner as set forth in claim 1, wherein said band is elastic, and wherein said pin projects from the back face as well as the front face of said first circular board.

3. The manipulative reckoner as set forth in claim 1, wherein said peripheral indicia of said second circular board visually indicates angular degrees of said predetermined angular intervals of said plurality of notches.

4. The manipulative reckoner as set forth in claim 1, wherein said peripheral indicia of said second circular board visually indicates decimal fractions of said predetermined intervals of said plurality of notches.

References Cited in the file of this patent UNITED STATES PATENTS 2,509,301 Henry May 30, 1950 2,529,413 Petersen Nov. 7, 1950 FOREIGN PATENTS 7,792 Great Britain Feb. ll, 1899 of 1898 713,371 Great Britain Aug. 18, 1954 

